4x^3-9xy^2=0

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Solution for 4x^3-9xy^2=0 equation: 


Simplifying
4x3 + -9xy2 = 0

Reorder the terms:
-9xy2 + 4x3 = 0

Solving
-9xy2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9y2 + 4x2) = 0

Factor a difference between two squares.
x((3y + 2x)(-3y + 2x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(3y + 2x)' equal to zero and attempt to solve:

Simplifying
3y + 2x = 0

Reorder the terms:
2x + 3y = 0

Solving
2x + 3y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

Subproblem 3
Set the factor '(-3y + 2x)' equal to zero and attempt to solve:

Simplifying
-3y + 2x = 0

Reorder the terms:
2x + -3y = 0

Solving
2x + -3y = 0

Move all terms containing x to the left, all other terms to the right.

Add '3y' to each side of the equation.
2x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
2x + 0 = 0 + 3y
2x = 0 + 3y
Remove the zero:
2x = 3y

Divide each side by '2'.
x = 1.5y

Simplifying
x = 1.5y
Solution
x = {0, -1.5y, 1.5y}

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